Inequality

Inequality is a measure of population equality designed to be consistent with the measure of geographic integrity based on chops due to node fragmentation. The correlation between the range and the number of geographic units suggests that the range decreases exponentially compared to the number of geographic units divided by the number of apportionment regions. The factor from the slope of that relationship gives approximately a decrease in the range by a factor of 10 for every additional 10 geographic units per region.

Modeling Inequality

A score for inequality could be based solely on this exponential inequality factor. Doing so overlooks the balance between the inequality and the chops. An approach that balances inequality with chops must consider the typical number of counties and regions in a state.

There are 3143 counties or county equivalents in the US for use as geographic units in this model. The New England states were analyzed based on towns instead of counties, and Alaska and Hawaii present other challenges to the model so those 8 states are excluded. In addition the independent cities in Virginia that are wholly surrounded by one county are excluded. That leaves 3023 county equivalents for 42 states, or an average of 72 counties per state.

There are 435 congressional districts in the US, but excluding New England, Alaska and Hawaii there are only 412. The remaining 42 states have 76 counties that are larger than a district and would be forced into a region with more than one district. There a total of 124 districts that could be embedded in a county, so the maximum number of regions is 288 for the 42 states. That is an average of just under 7 regions per state.

Region Inequality

The region inequality uses the average number of counties for a state and then creates a score based on the range that one would predict for the corresponding number of regions. Since each additional region could add a chop, this balances the effect of chops with inequality.

A state with 2 regions represents one split of the state. Using the 72 county average state and two regions, the correlation fit would predict a range of 6 for a score of 1. A second split into three regions results in a predicted range of 93 for a score of 2. This can be extended to any number of regions to predict a range for each. The ranges in the table below are rounded for convenience.

When using this inequality factor on a region plan, it is possible to create an artificially low score by grouping together regions with large deviations in opposite directions. For example suppose there are three districts with whole counties and deviations of +3100, -2600 and -500. Considered as three separate regions this would have a range of 5700 and an inequality of 11. If the first two districts were grouped together in one region it would have a deviation of +500, and the two regions have range of 1000. This would decrease the inequality from 11 to 5. Yet the district plan is unchanged and still has an inequality of 11. To prevent taking advantage of the region inequality score this way, the inequality factor for any district plan cannot exceed the inequality factor for the region plan. In this example the district plan would be forced to have a chop to reduce the deviations of the first two districts.

Inequality Factor

The inequality factor scores the range of a region or district plan. It assigns a score of 0 to an ideal plan with a range of 0 or 1. The score increases as the inequality increases. The inequality factor for a district plan must not exceed the factor for the corresponding region plan.

Inequality Factor	Range
0	0 - 1
1	2 - 10
2	11 - 100
3	101 - 400
4	401 - 900
5	901 - 1600
6	1601 - 2400
7	2400 - 3200
8	3201 - 4000
9	4001 - 4800
10	4801 - 5600
11	5601 - 6300
12	6301 - 7000
13	7001 - 7700
14	7701 - 8300
15	8301 - 8900
16	8901 - 9500
17	9501 - 10000
18	10001 - 10500
19	10501 - 11000
20	11001 - 11500